Give some examples of everyday vibrating objects. Which exhibit SHM, ab )wixm/mel)ha.su; scz/f.1qzib . 9t least approximats)mxszuh / qf .w/b9i;m b.ael) c.1izely?

Is the acceleration of a simple harmonic oscizfu r. gt+k3v)llator ever zero? If so, where?

Explain why the motion of a pis*;vv crryx7; kton in an automobile engine is approximately simple ha yv*r x;7;vkcrrmonic.

Real springs have mass. Will the true periodb+sm7gk 1t q. abvtbgi9fjci, n4217d and frequency be larger or smaller than given by the equations for a mass oscillating on the end of an idealized massless spring? Explainbg j.sq9 kt+ fa2cvdn17t74i1g,ibm b.

How could you double the maximum speed of a simple harmonic oscilla n5;9yrynerdg g +28:at3ghf u ghi8,wtor (SHO)?

A 5.0-kg trout is attached tolws zk+ u yr+o7.yb0s) the hook of a vertical spring scale, and then is released. Describe the scale reading as a function of timk0 )byoszw. +u+lsy7 re.

If a pendulum clock is accuratjs6k7 s o3n*qq j5egr c3v(ca.e at sea level, will it gain or lose time when taken to hige3v(k6c 7s 3naq5cs qo.j*rj gh altitude? Why?

A tire swing hanging from a branch reaches nearly to tjba1 za* ou q)l/7r2uxhe ground (Fig. 11–48). How could you estimate the height of the r)jl/2uqob x*z1ua 7abranch using only a stopwatch?

Why can you make water slosh back and forth in a pan only if you shb cp2q *(wqvj d4k6z:vake the pan at a certain fr4 c6bz*: kwd2qjqv(pvequency?

Give several everyday examples of resona 3,f4zfgzrc8q8 gbyu0 ybtg-(nce.

Is a rattle in a car ever a resonance phenxdix/l0z*t* 1t 8k vkcha mul :w y)6r.;9ylnxomenon? Explain.

Is the frequency of a simple periodic wave eqig6:zl xz6+n0 egug/ mual to the frequency of its source? +g0z6e:z6 lmigunxg / Why or why not?

Explain the difference between the speed of a transverse wave traveling down a ayrzd /s,f0k2 sru.lxu3i 2 7wcord and the speed of a ksy,7 wzf2dlu 3sarir x/ .u02tiny piece of the cord.

Why do the strings used for the lowest-frequency notes on a piano normallze58 i4uc+0l/bff3n evxk;(ou bgr/yy have b0b 4olkzg f+u/uv; r35ce8/e( yxf inwire wrapped around them?

What kind of waves do yo77o 8irx( z7okxtbx xn i)f fb269qde.u think will travel down a horizontal metal rod if you strike its end (a) vertically from above and (b) horizontally parallelkf bxizn.2x977q 8 7oofxdixr6(b te ) to its length?

Since the density of air decreases with an increase in temperature, but the bulshg: s i5ed;5jk modulus B is nearly independent of temperature, how would you expect the speed of sound waves in air to vary with temperatus5ejhsi ;g: 5dre?

Give two reasons why chzbq:0p23 bmah,o b-yircular water waves decrease in amplitude as they travel away from theb2 b :0-bq mz,aphoh3y source.

Two linear waves have the same amplitude and speed, and otherwise are ideb8;f;qn p +*y+uguv tfnqn u;qlba3/)ntical, except one has half the wavelength of the other. Which transmits more energvpnu;q b*+u 8bfl)t/f;3qgnqyau + n;y? By what factor?

When a sinusoidal wave crosses tgdt:-un2 az 7uhe boundary between two sections of cord as in Fig. 11–33, the frequency does not change (although the wavelength and vela-dgn2 z:uu7t ocity do change). Explain why.

If a string is vibrating i-rvtrs ov*ld8wq*p-qdn mw j)e; -)4 xn three segments, are there any places you could touch it with a knife blade without disturbing the qsjdrp d4)x r-)evnw 8mt-;ol*-wv *qmotion?

When a standing wave exists on a string, the vibrations of incident andrjb -7d qjzn(h gl2b26 reflected waves cancel at th 2lbhq 6djngz j27r-(be nodes. Does this mean that energy was destroyed? Explain.

If we knew that energy was being tra +/tig.6pc oa ;y76owyi63aw+dlgulu nsmitted from one place to another, how migho3u6 alw w.gg7i+c 6tu+ y6;l/dipayot we determine whether the energy was being carried by particles (material bodies) or by waves?

  If a particle undergoes SHM with amplitude 0.18 m, what is the total distal;hd7 70.wr fib;qij yst 4 +c7yc eypfs**-kjnce it travels in oj *bfccyes7f;swij 4yd7 *qi7;p.r ky0+ht- lne period?    m

  An elastic cord is 65 cm long when a weight of 75 N hangs from it bu 8 aerzzn494yft is 85 cm long when a weight of 180 N hangs from it. What is the “spring” conazeyzr 4fn9 84stant k of this elastic cord?    N/m

  The springs of a 1500-kg car compress 5.0 mm when its 68-kg drrq q7ptee c5 of9tm4a 32y;y,diver gets into the driver’s seat. If the car goes overom3ctte,97y;qq 4 eafrd2y5 p a bump, what will be the frequency of vibrations?$\approx$    Hz

  A fisherman’s scale stretches 3.6 cm when a 2.7-kg fish hangs ft qst 52/ chqc9g/zv7rd/l z8krom it. (a) What is the spring stic /8dqrk/v g5q2zs9 /chtl7z tffness constant $\approx$    N/m
(b) what will be the amplitude and frequency of vibration if the fish is pulled down 2.5 cm more and released so that it vibrates up and down? $\approx$    Hz (round to one decimal place)

  An elastic cord vibrates with a frequency of 3.0 Hz when a mass of 0.67 b0qoup0h lnug 97a,c0 kg is hung from it. What is l 9cah0n7u7bq,p 0 uogits frequency if only 0.38 kg hangs from it?    Hz

Construct a Table indicating the position x of the mass in Fig. 11–2 at2vqt mx 8u/u92rq oey9 times t = 0/m9u9 8 22yvr qoqxteu,t = $\frac{1}{4}T$,$\frac{1}{2}T$,$\frac{3}{4}T$,T and $\frac{5}{4}T$,where T is the period of oscillation. On a graph of x vs. t, plot these six points. Now connect these points with a smooth curve. Based on these simple considerations, does your curve resemble that of a cosine or sine wave (Fig. 11–8a or 11–9)?

  A small fly of mass 0.25 g is caught iexv:ko)ur1r,h*y3xs4 qd acqvw) 0+dn a spider’s web. The web vibrates predominately with ac) hx30rv* oa +eux4qrdqd k:1s v,y)w frequency of 4.0 Hz.
(a) What is the value of the effective spring stiffness constant k for the web?$\approx$    N/m (round to two decimal place)
(b) At what frequency would you expect the web to vibrate if an insect of mass 0.50 g were trapped?    Hz

  A mass m at the end of a spring vibb81l:oi9ma2u 9rox2:j a k aqxrates with a frequency of 0.88 Hz. When an additional 680-g mass is adde u xl1x:o2a8bkaqr9j2 mi:ao9d to m, the frequency is 0.60 Hz. What is the value of m?    kg

  A 0.60-kg mass at the end of a spring vibrates 3.9npxd.xf fh ub;/6fc10 times per second with an amplitude of 0;cx6 9ufn1/hdpbf f. x.13 m. Determine
(a) the velocity when it passes the equilibrium point,$\approx$    m/s(round to one decimal place)
(b) the velocity when it is 0.10 m from equilibrium, $\approx$ ±    m/s(round to one decimal place)
(c) the total energy of the system,$\approx$    J(round to one decimal place)
(d) the equation describing the motion of the mass, assuming that x was a maximum at x = (0.13π)cos(  πt)

  At what displacement from equilibrium is the speed n):yfu hj zp16of a SHO half the maximum valueuz6n f1yh: p)j?$\approx$    A

A mass attached to the end of sdrdu. 5/7szb fe8s5qa spring is stretched a distance $x_0$ from equilibrium and released. At what distance from equilibrium will it have acceleration equal to half its maximum acceleration?

  A mass of 2.62 kg stretches a vertical spring 0d+ya(fp;1mn87ac3pm .nxrn2 ;sag ck.315 m. If the spring is stretched an additional 0.130 m and releay(m 2kma 3gnc.dprasp1; nf nxc;a+78 sed, how long does it take to reach the (new) equilibrium position again?    s

  An object with mass 3.0 kg is attached to a spring with spring stifr6;7k6on.:;gkq1see q bf/p. tb xw dlfness constant k = 280 N/m and is executing simple harmonic motion. When the object is 0.020 m from its equilibrium position, it is moving with kk dnoe6/: l7r tfgswb.b6q;p;1e.qxa speed of 0.55 m/s
(a) Calculate the amplitude of the motion.    m
(b) Calculate the maximum velocity attained by the object.$\approx$    m/s (round to two decimal place)[Hint: Use conservation of energy.]

  It takes a force of 80.0 N to t zin6 ,gq,drnds.n:)compress the spring of a toy popgun 0.200 m to “load” a 0.180-kg ball. gts,q 6zd.i:, n)drnn With what speed will the ball leave the gun?    m/s

  A mass sitting on a horizontal, frictionless surface is attached to one end oftq2g 2ld2z(d6,ymab:+sku)5 wwt m z rl) tj)t a spring; the other end is fixed to a wall. 3.0 J of work is required to compress the spring by 0.12 m. If the mass is released from rest with the spring compressed, the mass experiences a maximum accer2k,td jtb6a ds2w w5)y(+m)z tu2l:) gq tlmzleration of 15 $m/s^2$ Find the value of
(a) the spring stiffness constant    N/m
(b) the mass.$\approx$    kg

  A 0.60-kg mass vibrates according to the equation x = 0.45cos6.e4 l(ng;gtz*phlbi r.34p) a e4t where x is in meters and t is in seconds. Determinznt4hib)* a geg.l(e3; p4rlpe
(a) the amplitude,    m
(b) the frequency, $\approx$    J(round to two decimal place)
(c) the total energy, $\approx$    J(round to one decimal place)
(d) the kinetic energy and potential energies when $\approx$    J(round to one decimal place)

  At what displacement from equilibr ( 6:c2rh1hse9yawarjium is the energy of a SHO half KE and half PEryra j9:(wec6s2a 1hh? ±    A

  If one vibration has 7.0 times the energp,2.9y2yrq bbvrnj ab;-u, a dy of a second, but their frequencies and masad;n9a pbyy,.bvu2, b2-rjqr ses are the same, what is the ratio of their amplitudes?   

  A 2.00-kg pumpkin oscillawvyv q*xa t 5bt*-6st1tes from a vertically hanging light spring once every 0.65t t5a*sb*-1txy vwvq6 s.
(a) Write down the equation giving the pumpkin’s position y (+ upward) as a function of time t, assuming it started by being compressed 18 cm from the equilibrium position (where ), and released. y = (   m)cos($\frac{2\pi t}{0.65s}$)
(b) How long will it take to get to the equilibrium position for the first time?    s
(c) What will be the pumpkin’s maximum speed?    m/s
(d) What will be its maximum acceleration, and where will that first be attained?   $m/s^2 $

A block of mass m is supported byx: :hshjx,*xs22 xmaw two identical parallel vertical springs, each with spring stiffness constant k (Fig. 11–a xj2xmh, ss :2:xhx*w49). What will be the frequency of vibration?

  A 300-g mass vibrates accordin(m0c)stjv3 f6l j10mgx zke0 1r8 yuidg to the equation x = 0.38sin6.5t where x is in meters and t is in seconds. Determij )g( 0cdi1s0 tr8z6lu 3m kmfvyjex10ne
(a) the amplitude,    m
(b) the frequency,    Hz
(c) the period,    s
(d) the total energy, $\approx$    J
(e) the KE and PE when x is 9.0 cm.$E_{potential}$ =    J $E_{kinetic}$ =    J($E_{kinetic}$round to two decimal place)
(f) Draw a careful graph of x vs. t showing the correct amplitude and period.

  Figure 11–50 shows two examplesi9w l qhr.peh4h.0zb8 of SHM, labeled A and B. For each, what is
(a) the amplitude,$A_A$ =    m $A_B$ =    m
(b) the frequency, $f_A$ =    Hz $f_B$ =    Hz
(c) the period? $T_A$ =    s $T_B$ =    s
(d) Write the equations for both A and B in the form of a sine or cosine.$x_A$ = (    m) sin($\frac{\pi}{2}t$) $x_B$ = (    m)cos ($\pi$t)

  At a 755-g mass at8c bh-svkr7i8 rest on the end of a horizontal spring (k = 124 N/m) is struck by a hammer, which gives the mass an initial speed of 2.kbc8rhs- 8v7i 96m/s Determine
(a) the period and frequency of the motion,    s    Hz
(b) the amplitude,    m
(c) the maximum acceleration,    $m/s^2$
(d) the position as a function of time, x = (    m)sin(4.08$\pi$t)
(e) the total energy.    J

A vertical spring with spring stiffness constant 305 N/yah , m5tvh1w(5okw j4m vibrates with an amplitude of ta5(mh, w4hykojw15v 28.0 cm when 0.260 kg hangs from it. The mass passes through the equilibrium point (x=0) with positive velocity at
(a) What equation describes this motion as a function of time?
(b) At what times will the spring have its maximum and minimum extensions?

A mass m is connected tqx l:msiriofj.w(5+ pa9)aw ;7e /gnd o two springs, with spring stiffness constants $k_1$ and $k_2$ as shown in Fig. 11–51. Ignore friction. Show that the period is given by
T=2 $\pi \sqrt{\frac{m}{k_{1}+k_{2}}}$ .

  A 25.0-g bullet strikes a 0.600-kg block attached to a fixey10r3q y+ma rod horizontal spring whose spring stiffness constant is q3yyro a1+rm0$ 7.7\times10^{3 }$ N/m The block is set into vibration with an amplitude of 21.5 cm. What was the speed of the bullet before impact if the bullet and block move together after impact?    m/s

  A bungee jumper with mass 65.0 kg jumps from a high br.mmysor )z (g,idge. After reaching his lowest point, he oscillates up and down, hitting a low point eight more times in 38.0 s. He finally comes to sm)zy.(m rg,o rest 25.0 m below the level of the bridge. Calculate the spring stiffness constant and the unstretched length of the bungee cord.
spring stiffness constant$\approx$    N/m(Round to the nearest integer)
unstretched length of the bungee cord    m

  A pendulum makes 36 vibrations in exaj)35bax 0f ) dx1okdeictly 60 s. What is its
(a) period,    s/cycle
(b) frequency?   Hz

  How long must a simple pendulum be if it is to mv7jsk wk 49p+vake exactly one swing per secondv9w7kjpv+k s4 ? (That is, one complete vibration takes exactly 2.0 s.)    m

  A pendulum has a period of 0.80 .pl )kn; y tsy:jrok0+s on Earth. What is its period on Mars, where the acceley r:+0n)ko.kly ;tspjration of gravity is about 0.37 that on Earth?    s

  What is the period of a lyxn28 z mc9*)zql(:thwk 8hssimple pendulum 80 cm long
(a) on the Earth,    s
(b) when it is in a freely falling elevator?

  The length of a simple pendulum is 0.760 m, the penduq 0jex 8z b*(gc)kjn5ulum bob has a mass of 365 grams, and it is released 5g* (8)kqjb ju0 nczexat an angle of 12.0 $^{\circ} $ to the vertical.
(a) With what frequency does it vibrate? Assume SHM. $\approx$    Hz(round to three decimal place)
(b) What is the pendulum bob’s speed when it passes through the lowest point of the swing?    m/s
(c) What is the total energy stored in this oscillation, assuming no losses?    J

  Your grandfather clock’s pendulum has a length of 0.9930 pr tdo3kh/*71v(d uq zm. If the clock loses half a minute per day, how should you adjust the length of the pendulumqhtd7( 1/d*k3v u ozpr? shortened by    mm.

Derive a formula for the maximum spkm5) -/4rfstyprq ri pt(4 iq5eed $v_{max}$ of a simple pendulum bob in terms of g, the length L, and the angle of swing $\theta_{0}$

  A clock pendulum oscillates at a frequency of 2.5 Hz. At it is released from v -rwvn0ysinz61( r9erest starting at an angle of 15yv0s ir1w(6n 9rv- zen $^{\circ} $ to the vertical. Ignoring friction, what will be the position (angle) of the pendulum at
(a) t = 0.25 s ,    $^{\circ} $
(b) t = 1.60 s ,    $^{\circ} $
(c) t = 500 s ?    $^{\circ} $
[Hint: Do not confuse the angle of swing $\theta$ of the pendulum with the angle that appears as the argument of the cosine.]

  A fisherman notices that wave crests pass the bow of his anchoreh 9,tcf. eeeq2d boat every 3.0 s. He measures the distance between two crests to be 6.5 m. How fast ar fceh 9et,e.2qe the waves traveling?    m/s

  A sound wave in air has a frequency of 262 Hz and travels with a spee *t:rr4. 0r+eafpqr1t gzx 6b ko/dt9kd of 343 m/s Hoqrko/r.t 0x 1 +*rdg k4abt:perfz6t9 w far apart are the wave crests (compressions)?    m

  (a) AM radio signals have frequenciljnwb8eoj3g w 9j31 d0/ku 6dres between 550 kHz and 1600 kHz (kilohertz) and travel with a s k3/ojwl jb9d13djg6e 0 u8wrnpeed of $ 3\times10^{8 }$ m/s What are the wavelengths of these signals?    m to    m(b) On FM, the frequencies range from 88.0 MHz to 108 MHz (megahertz) and travel at the same speed; what are their wavelengths?   m to    m

  Calculate the speed of longitudinal waves ,,wrgik+iq 50 k qe+g1 g,ry7ib /rvyuin
(a) water,    m/s
(b) granite,    m/s
(c) steel.    m/s

  Two solid rods have the same elasticf u(3kl)0bsty6;czzg modulus, but one is twice as dense as the other. In which rod wic;)tsf6 kuzyb03(g lzll the speed of longitudinal waves be greater, and by what factor?   

  A cord of mass 0.65 kg is stretched between two supports 28 m apart. z-t o-v los3:oIf the tension in the cord is 150 N, how long will it take a pulse to travel from one supp3o- s:ovz tlo-ort to the other?    s

  A ski gondola is conne 9yq0qorqu;4 gcf,(gn: mga2octed to the top of a hill by a steel cable of length 620 m and diameter 1.5 cm. As the gondola comes to the end of,0f:qmq9 ua(g cyor24on; gqg its run, it bumps into the terminal and sends a wave pulse along the cable. It is observed that it took 16 s for the pulse to return.
(a) What is the speed of the pulse? (Round to the nearest integer)$\approx$    m/s
(b) What is the tension in the cable?    N

  A sailor strikes the side o2ve.c) mf t abblr2/w5f his ship just below the surface of the sea. He hears the echo of the wave reflected from the ocean floor directly below 3.0 s later. How deep isbc r5/2lwe a)t2 vb.mf the ocean at this point?    m

  P and S waves from an earthquake travel at dihdw:.:vgb2o 9o*szk.z,( k nxh/hf-2 rtmmtafferent speeds, and this difference helps in locating the earthquake “epicenter” (where the disturbwmhzn/* f st, bg9(v:tkoo-a2r z.dm2x:.hkhance took place).
(a) Assuming typical speeds of 8.5km/s and 5.5km/s for P and S waves, respectively, how far away did the earthquake occur if a particular seismic station detects the arrival of these two types of waves 2.0 min apart?    km
(b) Is one seismic station sufficient to determine the position of the epicenter? Explain.

  An earthquake-produced surface wave can be aptop rsws9t)nh:5s3p , proximated by a sinusoidal transverse wave. Assuming a frequency of 0.50 Hz (typical of earthquakes, which actually include a mixtutopshsr,tw3ns9 p5:)re of frequencies), what amplitude is needed so that objects begin to leave contact with the ground? [Hint: Set the acceleration a>g]    m

  What is the ratio of (a) the intensities, and (b) the amplitudes, of an earthqua;x :pszsh2 hoz+g3ov 0ke P wave passing through the h ;:o0 3+h2ovzspzgsxEarth and detected at two points 10 km and 20 km from the source?(a)    (b)   

  The intensity of an earthquake wave passing through the Earth is mea pk 6f,mr1lkdp1 ivj 66n)2p- wa0 u5agnycrx6sured to be r6 5d1f l )vr,kx wi0k6gujc p126apm y6pn-na$ 2\times10^{6 }J/m^2$ at a distance of 48 km from the source.
(a) What was its intensity when it passed a point only 1.0 km from the source?(round to one decimal place)$\approx$    $ \times10^{9 }W/m^2$
(b) At what rate did energy pass through an area of $5m^2$ at 1.0 km?    $ \times10^{10 }W$

  Two earthquake waves of the same frequency travel through the same portion of tp.4bodhkgw*wy. n5n 8 kv 7me1he Earth, but one is carrying twice the energy. What is the ratio of the amplitudes of the two4*d1 8ov n gkw..ybnewkmp 7h5 waves?   

  Two waves traveling along a stretched string have the n8snf 3d,5 nuusame frequency, but one transports three times the power of the other. What is the ratio of the sn, unfd5nu 83amplitudes of the two waves?   

  A bug on the surface of,lh r4dgn:8i o a pond is observed to move up and down a total vertical distance of 6.4o dinr8h:l,g 0 cm, from the lowest to the highest point, as a wave passes. If the ripples decrease to 4.5 cm, by what factor does the bug’s maximum KE change?   

The two pulses shown in Fig. 11–52 are moving toward each other. g94 +ywbw z5acv mdm0g0ek; )x(a) Sketch the se49 wvkzm+0gd5)xb mwc 0;ay ghape of the string at the moment they directly overlap. (b) Sketch the shape of the string a few moments later. (c) In Fig. 11–36a, at the moment the pulses pass each other, the string is straight. What has happened to the energy at this moment?

  If a violin string vibrates at 440 Hz u0f 3hkynke-0s; vh;u as its fundamental frequency, what are the frequencies of the first 0-s30h ;k veuhk;nufy four harmonics?$f_1$ =    Hz $f_2$=    Hz $f_3 $ =    Hz $f_4 $=    Hz

  A violin string vibrates at 294+(( tthqrr31+ lmcm5fw:adg e Hz when unfingered. At what frequency will it vibrate if it is fingered one-third of the way down from the end? (That is, only two-thirds of the string vibrates as a sth 1rlwg rm3e(:atcfq m d+t+(5anding wave.)    Hz

  A particular string racb 2)(qa y1ga-b(lpresonates in four loops at a frequency of 280 Hz. Name at least three other frequencies at which it will reso(rplb)a qgba(1 2yc-a nate. $f_1$ =    Hz $f_2$ =    Hz $f_3 $ =    Hz $f_5 $ =    Hz

  The velocity of waves on a string is 92m/s*80( scozv+cb z1f k8roxs0cg If the frequency of standing waves is 475 Hz, how far apart are two adja1(sczr z*008 b xsgcck8+ vfoocent nodes?   m

  If two successive overtones of a vibrating string are 280 Hz and 350 Hz, what i:o77v1jxcfao6e kr 4u d (kk;zs the frequency of the fundamentav 47k(1krouxf o;cz a: 76jdkel?    Hz

  A guitar string is 90 cm long and has a mass ofn eukwg/.;2zc 3.6 g. The distance from the bridge to the support post is L = 62cm and the string is under a tension ofu 2;cz/enw g.k 520 N. What are the frequencies of the fundamental and first two overtones?    Hz

  A particular guitar string is suppose dy,;+p6p cz3aem ixhr7sjl;-d to vibrate at 200 Hz, but it is measured to vibrate at 20c+7,lj s; ;yard ph mpzeix6-35 Hz. By what percent should the tension in the string be changed to correct the frequency?So the three frequencies are,    Hz    Hz    Hz to 2 significant figures.

  A particular guitar string is supposed to vibrate at 200k9p0-;9boj z aibl jzz3:6zxc Hz, but it is measured to vibrate at 205 Hz. By what percent should the tension in the string be changed to correct the frequency? -k:z06jz3jp99 cabox z;blzidecreased by    %

  One end of a horizontal string i55d* xqg ujl6hs attached to a small-amplitude mechanical 60-Hz vibrator. The string’s mass per unit lenx*jl 655qdhgu gth is $3.9 \times10^{ -4}$ kg/m The string passes over a pulley, a distance L = 1.50 m away, and weights are hung from this end, Fig. 11–53. What mass m must be hung from this end of the string to produce
(a) one loop,(round to one decimal place) $\approx$    kg
(b) two loops,    kg
(c) five loops of a standing wave? Assume the string at the vibrator is a node, which is nearly true.   kg

  In Problem 59, the length of the string mayybk7 avmz*e1ubm 3:8d be adjusted by moving the pulley. If the hanging mass m is fixed at 0.080 kg, how many different standing wave patk87bu m zym3a*e1db: vterns may be achieved by varying L between 10 cm and 1.5 m?   

  When you slosh the watpust*t vf pb lx54z3g/t(p dw/,jqnj1 mm,y-1 er back and forth in a tub at just the right frequency, the water alternately rises and falls at each end, remaining relatively calm at the center. Suppose the frequency to produce such a standing wave in a 65-cm-wide tub is 0. pwm,t5t-dxm/ yn /glujt4q, v(fs1*zbp 13pj85 Hz. What is the speed of the water wave?    m/s

  An earthquake P wave trav2:s/ ghot9yopp ,gme4eling at k.0 km/s strikes a boundary within the Earth between e9pgt,:4g 2/oopysmhtwo kinds of material. If it approaches the boundary at an incident angle of 47 $^{\circ} $ and the angle of refraction is 35 $^{\circ} $, what is the speed in the second medium?    km/s

  Water waves approach an underwater “shelf” where thty jl9q -q;v-be velocity changes from 2.8 m/s to 2.1 m/s If the incident wave crests make a 34 -ybj -9tql;qv$^{\circ} $ angle with the shelf, what will be the angle of refraction?    $^{\circ} $

  A sound wave is traveling in warm air when it hits a layer of cold, eoy (a3ed:f6yw1cwn 0 dense air. If then1 w0(3c6: yfye waode sound wave hits the cold air interface at an angle of 25$^{\circ} $, what is the angle of refraction? Assume that the cold air temperature is $ - 10 ^{\circ} C$. and the warm air temperature is $ + 10 ^{\circ} C$. The speed of sound as a function of temperature can be approximated by v=(331+0.60T) m/s where T is in $ -10 ^{\circ} C$.    $^{\circ} $

  A longitudinal earthquake wave strv fm:rce/,9xrikes a boundary between two types of rock at a 38 e / :9fxc,vrmr$^{\circ} $ angle. As the wave crosses the boundary, the specific gravity of the rock changes from 3.6 to 2.8. Assuming that the elastic modulus is the same for both types of rock, determine the angle of refraction.    $^{\circ} $

  A satellite dish is about 0.5 m in diameter. Atdjf*uo1 ;e-p ccording to the user’s manual, the dish has to be pointed in thepue1oj *d-f;t direction of the satellite, but an error of about 2 $^{\circ} $ is allowed without loss of reception. Estimate the wavelength of the electromagnetic waves received by the dish.    m

  A tsunami of wavelength 250 km and velohc7vvts74(v jsg rv* (city 750 km/h travels across the Pacific Ocean. As it approaches Hawaii, people o 74(schvj t(*rvvs7gvbserve an unusual decrease of sea level in the harbors. Approximately how much time do they have to run to safety? (In the absence of knowledge and warning, people have died during tsunamis, some of them attracted to the shore to see stranded fishes and boats.)    min

  An energy-absorbing car bumper has a spring stiffness constant znmlf8vux4,9s3 6r bb2oaktqi uw.7, of 550 kN/m Find the maximum compression of the bumper if the car, with mass 1500 kg, collides with a wall at a speed of 2.2 m/s (appnbmuu7396q.28fkti z b la,v,rwx4so roximately 5 mi/h). [Hint: Use conservation of energy.]    m

  A 65-kg person jumps from a window to a fire net 18 m below, which stretches xwii n8v *1:rvo(m/; hesc2 sgthe net 1.1 m. Assume2romi h/cn :vw i;v*8sx1e(gs that the net behaves like a simple spring, and
(a) calculate how much it would stretch if the same person were lying in it.    m
(b) How much would it stretch if the person jumped from 35 m?    m

  A mass m is gently placed on the end of a freely hangi82jk34uhs *euqs*pa2 ikj.k 4i3htbb ng spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the osc8s4.22 4uapb3*hsejk j3uhk *tibq kiillation?    Hz

  A 950-kg car strikes a huge spring at a speed of 22 (r8yl)4d p;yj8ir ,kb bgq:fn m/s (Fig. 11–54), compressing the spring 5.0 m. (a) What is the spring stiffness constant of the b, bn4rlpj:i8) fk8gdyy rq(;spring?    N/m (b) How long is the car in contact with the spring before it bounces off in the opposite direction?    s

  When you walk with a cup of coffee (diameter 8 cm) at jusp9tlj8m3v8 af t the right pace of about 1 step per second, the coffee sloshes more and more until eventually iptf 3j8avl 8m9t starts to spill over the top (Fig. 11–55). Estimate the speed of waves in the coffee.    cm/s

  The ripples in a certain groove 10.8 cm from the center o+w wpb;3gkjn1 f a 33-rpm phonograph recorn1p+bkwj 3g ;wd have a wavelength of 1.70 mm. What will be the frequency of the sound emitted?    Hz

  A 2.00-kg mass vibrates according to the equation x=0pa.; -vo0i hznmv/eovw -b8 n5.650cos7.40t where x is in meters and t in - vamehzp/w- 5ono0;bv8.inv seconds. Determine
(a) the amplitude,    m
(b) the frequency,(round to two decimal place)$\approx$    Hz
(c) the total energy,(round to one decimal place)$\approx$    J
(d) the kinetic energy and potential energy when x=0.260 m.(round to one decimal place) PE$\approx$    J KE =    J

  A simple pendulum oscillates w0af3 ktb;l.b0vuunye8z: o-k ith frequency f. What is its frequency if it accelerates at 0.50g. -vk l : 008ue;yozn3ftkbbau (a) upward,    f
(b) downward?    f

  A 220-kg wooden raft floats on a lake. When a(6uk wlgo,e6whsg 8)a 75-kg man stands on the raft, it sinks 4.0 cm deeper into the water. When he steps off, th)(w6kes 6ga,hglwou 8e raft vibrates for a while.
(a) What is the frequency of vibration?(round to one decimal place) $\approx$    Hz
(b) What is the total energy of vibration (ignoring damping)?(Round to the nearest intege) $\approx$    J

  Two strings on a musical iqw+fd3yjs- k5c dxj-1nstrument are tuned to play at 392 Hz (G) and 440 Hz (A).qsdj1w5j3d+k-y- f xc
(a) What are the frequencies of the first two overtones for each string? G : $f_2$=    Hz $f_3$=    Hz A : $f_2$=    Hz $f_3$=    Hz
(b) If the two strings have the same length and are under the same tension, what is the ratio of their masses ($m_{\mathrm{G}}/m_{\mathrm{A}}$)   
(c) If the strings instead have the same mass per unit length and are under the same tension, what is the ratio of their lengths($L_{\mathrm{G}}/L_{\mathrm{A}}$)   
(d) If their masses and lengths are the same, what must be the ratio of the tensions in the two strings?   

Consider a sine wave traveling downr;+vvc;3nq zn the stretched two-part cord of Fig. 11–33. Determine a formula (a) for the ratio of the speeds of the wave in the heavy section versus that in the lighter section, and (b) for the ratio of the wavelengths in the two sections. (The frequency is the same in both sectionsn;vv+ nq;c3zr. Why?) (c) Is the wavelength greater in the heavier section of cord or the lighter?

  A tuning fork vibrates at a frequency os( -tpuapc - ;nqf2uibf+ 7q,ff 264 Hz, and the tip of each prong moves 1.8 mm to either side of center. Calf s-qu2fb fn;paq-c piu+( t7,culate
(a) the maximum speed    m/s
(b) the maximum acceleration of the tip of a prong.    $m/s^2$

A diving board oscillates with siseqcb vkz3p. l- + n) u+qmv1lnh3f)n7 4y9zbsmple harmonic motion of frequency 1.5 cycles per second. What is the maximum amplitude with which the end of the board can vibrate in order that a pebble placed there (Fig. 11–56) will not lo yq-)lhzq13v)se 4lnvnkfmb p 3bnc z.s+9u7 +se contact with the board during the oscillation?

A string can have a “f gt51i; -tzzjyree” end if that end is attached to a ring that can slide without friction on a vertical pole (Fig. 11–57). Determine the wat-z g5z1 jyt;ivelengths of the resonant vibrations of such a string with one end fixed and the other free.

  A “seconds” pendulum has a period of exactly 2.000 s — each one-way sw7yinv4 af m6d9ing takes 16 4d7 yvifn9am.000 s.
(a) What is the length of a seconds pendulum in Austin, Texas, where $g=9.793\mathrm{m/s}^{2}$    m
(b) If the pendulum is moved to Paris, where $g=9.809\mathrm{m/s}^{2}$ by how many millimeters must we lengthen the pendulum?    mm
(c) What would be the length of a seconds pendulum on the Moon, where $g=1.62\mathrm{m/s}^{2}$    m

A mass hanging from a spring can oscivur* n: bfot15llate in the vertical direction or can swing as a pendulum of small amplitude, but not both at the same time. Which one is longer, the period of the vertical oscillations or the period 1o5 tn f:*uvrbof the horizontal swings, and by what amount? [Hint: Let $l_0$ be the length of the unstretched spring, and L be its length with the mass attached at rest.]

  A block with mass $M=5.0\mathrm{kg}$ rests on a frictionless table and is attached by a horizontal spring $\begin{pmatrix}k=130\mathrm{N/m}\end{pmatrix}$ to a wall. A second block, of mass $m=1.25\mathrm{kg}$ rests on top of M. The coefficient of static friction between the two blocks is 0.30. What is the maximum possible amplitude of oscillation such that m will not slip off M?    m

  A 10.0-m-long wire of mass 123 g : 6oj l5e9udmeis stretched under a tension of 255 N. A pulse is generated at one end, and 20.0 ms later a second pulse is generated at the opposite end. Where will the two pulses first o em :9d6eulj5meet?    m

A block of mass M is suspendo3(do+j ex 8uxed from a ceiling by a spring with spring stiffness constant k. A penny ode x uo(ox3+j8f mass m is placed on top of the block. What is the maximum amplitude of oscillations that will allow the penny to just stay on top of the block? (Assume $m \ll M$)

  A crane has hoisted a 1200-k:.xsy0 9p qephsuo6 :cg car at the junkyard. The steel crane cable is 22 m long and has a diameter of 6.4 mm. A breeze starts the car bouncing at the end of the cable. What is the period o9 ps:y.q :6u0hepxscof the bouncing? [Hint: Refer to Table 9–1.]    s

  A block of jello rests on a plate as shown in Fig. 11–58 (which also gives k:n-qf q*s:1p/qmia1+de svvuk 6wgg:ml ; r8 the dimensions of the block). You push it sideways as shown, and then you let go. The ja:qgiev:6 k8:lnp+u*gk dsr;1m 1-q/qfv swm ello springs back and begins to vibrate. In analogy to a mass vibrating on a spring, estimate the frequency of this vibration, given that the shear modulus (Section 9–5) of jello is 520 $N/m^2$ and its density is 1300 $kg/m^3$    Hz